Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26042092 | C2 | semidirect |
| 2. #26042088 | C2 | semidirect |
| 3. #26042084 | C2 | semidirect |
| 4. #26041664 | C2 | semidirect |
| 5. #26041550 | C2 | semidirect |
| 6. #26041545 | C2 | semidirect |
| 7. #26041455 | C2 | semidirect |
| 8. #26041454 | C2 | semidirect |
| 9. #26041395 | C2 | semidirect |
| 10. #26041394 | C2 | semidirect |
| 11. #473×C181 | C2 | semidirect |
| 12. #19153864 | C22 | semidirect |
| 16. #19153847 | C22 | semidirect |
| 19. #19153844 | C22 | semidirect |
| 27. C2×#15668436 | C22 | semidirect |
| 31. #19153824 | C22 | semidirect |
| 32. #19153822 | C22 | semidirect |
| 33. #19153805 | C22 | semidirect |
| 34. #19153751 | C22 | semidirect |
| 36. #19153742 | C22 | semidirect |
| 37. #19153742 | C22 | semidirect |
| 38. #19153732 | C22 | semidirect |
| 39. C8×Dic181 | C22 | semidirect |
| 41. C2×Q16×C181 | C22 | semidirect |
| 43. #108×C181 | C22 | semidirect |
| 44. #101×C181 | C22 | semidirect |
| 149. C181 | #3290 | semidirect |
| 155. #473 | D181 | semidirect |
| 178. C2×Q16 | C2×D181 | semidirect |
| 188. #108 | C2×D181 | semidirect |
| 192. #101 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042092 | 2 |
| #26042088 | 2 |
| #26042084 | 2 |
| #26041664 | 2 |
| #26041550 | 2 |
| #26041545 | 2 |
| #26041455 | 2 |
| #26041454 | 2 |
| #26041395 | 2 |
| #26041394 | 2 |
| #473×C181 | 2 |
| #3290 | 181 |